Percentages and Discounts: Civil Service Exam Guide

Percentages and discounts are among the most frequently tested topics in the Civil Service Exam (CSE). These questions appear in the Numerical Ability or Quantitative section and require examinees to understand how percentages work, how to convert fractions and decimals into percentages, how to compute increase or decrease, and how to determine the final price after a discount. Mastering these concepts significantly improves your calculation accuracy and speed, which are crucial during the exam.

This guide provides a clear breakdown of all major ideas related to percentages and discounts, including practical examples, step-by-step solutions, and techniques to avoid common mistakes. Whether you are reviewing for the CSE Professional or Sub-Professional level, this guide builds the foundation you need to handle numerical problems with confidence.

What Is a Percentage?

A percentage represents a fraction out of 100. The symbol % means “per hundred.”

For example:

• 25% means 25 out of 100
• 8% means 8 out of 100
• 100% means the whole or one complete unit

Percentages allow comparisons even when quantities differ. This is why many exam questions use percentages to measure growth, reduction, profit, loss, and discounts.

Converting Between Fractions, Decimals, and Percentages

Understanding conversions is essential for solving percentage questions quickly.

Converting Fractions to Percentages

Multiply the fraction by 100%.

Example: (3/5) × 100 = 60%

Converting Decimals to Percentages

Multiply the decimal by 100.

Example: 0.45 × 100 = 45%

Converting Percentages to Decimals

Divide by 100.

Example: 72% ÷ 100 = 0.72

Converting Percentages to Fractions

Write the percentage over 100 and simplify.

Example: 40% = 40/100 = 2/5

These conversions help you switch forms quickly depending on what the problem requires.

Finding the Percentage of a Number

Use the formula:

Percentage of a number = Rate × Base

Where:

• Rate = the percentage
• Base = the original number

Example:
What is 25% of 300?

25% = 0.25
0.25 × 300 = 75

Percentage Increase and Percentage Decrease

Percentage increase and decrease questions frequently appear in the exam. These questions involve comparing the old value with the new value.

Percentage Increase Formula

Percentage Increase = ((New Value – Old Value) / Old Value) × 100

Percentage Decrease Formula

Percentage Decrease = ((Old Value – New Value) / Old Value) × 100

Example (Increase):
A price increases from ₱200 to ₱260. What is the percentage increase?

((260 − 200) / 200) × 100 = 30%

Example (Decrease):
A price drops from ₱500 to ₱400. What is the percentage decrease?

((500 − 400) / 500) × 100 = 20%

Understanding Discounts

A discount is a reduction from the original price. It is usually expressed as a percentage.

Discount Formulas

Discount Amount = Original Price × Discount Rate

Sale Price = Original Price − Discount Amount

Example:
A bag originally costs ₱1,200 and is discounted by 15%. What is the sale price?

Step 1: Compute discount amount.
15% of 1,200 = 0.15 × 1,200 = 180

Step 2: Subtract from original.
1,200 − 180 = ₱1,020

Successive Discounts

Stores sometimes offer multiple discounts, such as “20% off, then an additional 10% off.” These are not added directly.

You must apply the second discount to the already discounted price.

Example:
A jacket costs ₱2,000 with successive discounts of 20% and 10%.

Step 1: Apply 20% discount
20% of 2,000 = 400 → new price = 2,000 − 400 = 1,600

Step 2: Apply 10% discount
10% of 1,600 = 160 → final price = 1,600 − 160 = ₱1,440

Finding the Original Price Before Discount

Sometimes the problem gives the sale price after discount, and you need to find the original price.

Formula:

Original Price = Sale Price ÷ (1 − Discount Rate)

Example:
A shirt sells for ₱720 after a 20% discount. What was the original price?

Original Price = 720 ÷ 0.80 = 900
Original price = ₱900

Discount Rate When You Know Original Price and Sale Price

If the original price and sale price are known, you can find the discount rate.

Formula:

Discount Rate = ((Original Price − Sale Price) / Original Price) × 100

Example:
Original Price: ₱1,500
Sale Price: ₱1,200

Discount = 1,500 − 1,200 = 300
Discount Rate = (300 ÷ 1,500) × 100 = 20%

Real-Life Applications on the Civil Service Exam

Percentage and discount problems often appear in situations such as:

• Salary increases
• Price reductions
• VAT and taxes
• Budgeting scenarios
• Comparing data sets
• Percentage change over time

CSE examiners design questions that require quick mental math, so understanding shortcuts is essential.

Useful Shortcuts for Exam

1. 10% is easy

Move the decimal one place to the left.
Example: 10% of 450 is 45.

2. 5% is half of 10%

Example: 5% of 450 = half of 45 = 22.5

3. 1% is the number divided by 100

Example: 1% of 450 = 4.5

4. Combine shortcuts

Example: 16% of 250 = 10% + 5% + 1%

• 10% of 250 = 25
• 5% of 250 = 12.5
• 1% of 250 = 2.5

Total = 25 + 12.5 + 2.5 = 40

Common Mistakes to Avoid

• Adding successive discount percentages directly
  Wrong: 20% + 10% = 30%
  Correct: Apply one discount after another.
• Forgetting to convert percent to decimal
  Remember that 20% is 0.20, not 20.
• Applying the second discount to the original price
  The second discount must use the discounted price.
• Mixing up increase vs. decrease formula
• Trying to compute everything manually without shortcuts

Practice Examples with Solutions

Example 1

What is 12% of 850?

12% = 0.12
0.12 × 850 = 102

Example 2

A price increases from ₱900 to ₱1,080. What is the percentage increase?

Increase = 1,080 − 900 = 180
Rate = (180 ÷ 900) × 100 = 20%

Example 3

A laptop costing ₱35,000 is discounted by 18%. What is the sale price?

Discount = 18% of 35,000 = 0.18 × 35,000 = 6,300
Sale Price = 35,000 − 6,300 = ₱28,700

Example 4

After a 25% discount, a gadget sells for ₱3,600. What was the original price?

Original Price = 3,600 ÷ 0.75 = ₱4,800

Example 5

A store applies two successive discounts of 30% and 20% on a ₱5,000 item. What is the final price?

First discount:
30% of 5,000 = 1,500 → new price = 5,000 − 1,500 = 3,500

Second discount:
20% of 3,500 = 700 → final price = 3,500 − 700 = ₱2,800

Why This Topic Matters in the Civil Service Exam

Percentage and discount questions:

• Are predictable and follow standard patterns
• Require no advanced formulas
• Can be solved quickly with practice
• Offer high scoring potential

If you master basic percentage calculations and discount logic, you can answer these questions in less than 20 seconds each, leaving more time for difficult items.

Tips for Answering Percentage Questions Faster

• Memorize common percentages (10%, 20%, 25%, 50%).
• Convert complex fractions to percentages before solving.
• Round numbers when allowed to estimate quickly.
• Write intermediate results to avoid confusion.
• Practice mental math daily.

Problem Sets

Set: Percentages and Discounts – Civil Service Exam Practice

Instructions:
Choose the correct answer for Items 1–10. For Items 11–20, write the final numerical answer only (no need to show solution in the exam, but practice showing it while reviewing).

1. What is 18% of 250?
   A. 35
   B. 40
   C. 45
   D. 50

2. What is 7.5% of 800?
   A. 50
   B. 55
   C. 60
   D. 65

3. What percent of 400 is 80?
   A. 10%
   B. 15%
   C. 20%
   D. 25%

4. A value increases from 1,200 to 1,500. What is the percentage increase?
   A. 20%
   B. 22%
   C. 25%
   D. 30%

5. A quantity decreases from 960 to 720. What is the percentage decrease?
   A. 20%
   B. 22.5%
   C. 25%
   D. 30%

6. A shirt costs ₱900 and is on sale at 15% discount. What is the sale price?
   A. ₱750
   B. ₱765
   C. ₱780
   D. ₱800

7. A pair of shoes costs ₱2,500. During a sale, it is given a 20% discount followed by an additional 10% discount on the reduced price. What is the final price?
   A. ₱1,750
   B. ₱1,800
   C. ₱1,900
   D. ₱2,000

8. After a 30% discount, a bag is sold for ₱1,750. What was its original price?
   A. ₱2,250
   B. ₱2,400
   C. ₱2,500
   D. ₱2,800

9. A gadget’s marked price is ₱8,000. It is sold for ₱6,000. What is the discount rate?
   A. 20%
   B. 22.5%
   C. 25%
   D. 30%

10. A store advertises “Buy now and save 12.5%!” If the original price of a rice cooker is ₱3,200, how much is the discount amount?
    A. ₱350
    B. ₱375
    C. ₱400
    D. ₱425

11. A student scored 36 out of 45 in a quiz. What is her score in percent? (Round to the nearest whole percent.)

12. A barangay’s population increased from 8,000 to 9,200 in one year. What is the percentage increase?

13. A jacket costing ₱3,600 is discounted by 18%. What is the sale price?

14. A grocery bill is ₱2,450. If a customer gets a 10% discount coupon, how much does he pay after the discount?

15. A machine’s value depreciated from ₱50,000 to ₱37,500. What is the percentage decrease?

16. After receiving a 25% discount, a customer pays ₱2,250 for a certain item. What was the original price?

17. A store offers successive discounts of 15% and 10% on a laptop with a tagged price of ₱40,000. What is the final selling price?

18. An employee’s monthly salary is increased from ₱22,000 to ₱25,300. What is the percentage increase? (Round to the nearest tenth of a percent.)

19. A water bill increased by 12% to ₱1,568. What was the original bill before the increase?

20. A cellphone originally priced at ₱18,000 is offered at 20% discount. Additionally, the customer uses a voucher for another 5% discount on the already discounted price. What is the final amount to be paid?

Answer Keys

Items 1–10 (Multiple Choice)

1. C

2. C

3. C

4. C

5. C

6. B

7. B

8. C

9. C

10. B

Solutions / Final Answers for Items 11–20

36 ÷ 45 = 0.8 = 80%

Increase = 9,200 − 8,000 = 1,200
1,200 ÷ 8,000 × 100 = 15%
15%

18% of 3,600 = 0.18 × 3,600 = 648
3,600 − 648 = ₱2,952

10% of 2,450 = 245
2,450 − 245 = ₱2,205

Decrease = 50,000 − 37,500 = 12,500
12,500 ÷ 50,000 × 100 = 25%
25%

Let original price = x
After 25% discount: 0.75x = 2,250
x = 2,250 ÷ 0.75 = ₱3,000

First discount 15%:
15% of 40,000 = 6,000 → new price = 40,000 − 6,000 = 34,000

Second discount 10% on 34,000:
10% of 34,000 = 3,400 → final price = 34,000 − 3,400 = ₱30,600

Increase = 25,300 − 22,000 = 3,300
3,300 ÷ 22,000 × 100 ≈ 15.0%
15.0% (approx.)

Let original bill = x
12% increase → 1.12x = 1,568
x = 1,568 ÷ 1.12 = ₱1,400

First discount 20%:
20% of 18,000 = 3,600 → new price = 18,000 − 3,600 = 14,400

Second discount 5% on 14,400:
5% of 14,400 = 720 → final price = 14,400 − 720 = ₱13,680

Civil Service Exam Philippines: Complete Preparation and Passing Guide